# Point A is at (2 ,-6 ) and point B is at (-8 ,-3 ). Point A is rotated pi/2  clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?

Feb 6, 2018

New coordinate of color(red)(A (-5, -2)

Distance changed (increase) between A & B by $\left(\frac{\pi}{2}\right)$ clockwise rotation of A about the origin is $\textcolor{g r e e n}{\sqrt{109} - \sqrt{10} \approx 7.28}$

#### Explanation:

A (2, -6), B(-8, -3)

Point A rotated clockwise about the origin by $\frac{\pi}{2}$

Both x & y are negative.That means, x -> -y and y -> x.

$A \left(\begin{matrix}2 \\ - 5\end{matrix}\right) \to A ' \left(\begin{matrix}- 5 \\ - 2\end{matrix}\right)$

$A B = \sqrt{{\left(2 - \left(- 8\right)\right)}^{2} + {\left(- 6 - \left(- 3\right)\right)}^{2}} = \sqrt{109}$

$A ' B = \sqrt{{\left(- 5 - \left(- 8\right)\right)}^{2} + {\left(- 2 - \left(- 3\right)\right)}^{2}} = \sqrt{10}$

Distance changed between A & B by th#pi/2) clockwise rotation of A about the origin is

$A ' B - A B = \textcolor{g r e e n}{\sqrt{109} - \sqrt{10} \approx 7.28}$